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A098299 Member r=14 of the family of Chebyshev sequences S_r(n) defined in A092184. 0

%I

%S 0,1,14,169,2016,24025,286286,3411409,40650624,484396081,5772102350,

%T 68780832121,819597883104,9766393765129,116377127298446,

%U 1386759133816225,16524732478496256,196910030608138849

%N Member r=14 of the family of Chebyshev sequences S_r(n) defined in A092184.

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-13,1).

%F a(n)= (T(n, 6)-1)/5 with Chebyshev's polynomials of the first kind evaluated at x=6: T(n, 6)=A023038(n)= ((6+sqrt(35))^n + (6-sqrt(35))^n)/2.

%F a(n)= 12*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.

%F a(n)= 13*a(n-1) - 13*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=14.

%F G.f.: x*(1+x)/((1-x)*(1-12*x+x^2)) = x*(1+x)/(1-13*x+13*x^2-x^3) (from the Stephan link, see A092184).

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 18 2004

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Last modified September 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)